Answer:
a. The surface area is
b. The radius is 8 cm
Step-by-step explanation:
The surface area of a beachball is modeled by the function
Where x is the radius of the beachball.
It's given that a beachball of radius 12 cm has a surface area of
This information will allow us to find the value of a by substituting in the model:
Dividing by 144:
a = 1809.56/144
a = 12.57
The model is now:
Now we can solve parts a and b:
a . Find the surface area of a beachball of radius x=15 cm
The surface area is
b. Find the radius of a beachball with a surface area of
We need to solve:
Dividing by 12.57:
Thus:
x=8 cm
The radius is 8 cm
We could use the formula, derive the formula, or just work it out for this case. Let's do the latter.
The distance of a point to a line is the length of the perpendicular from the line to the point.
So we need the perpendicular to 5x-4y=10 through (-1,3). To get the perpendicular family we swap x and y coefficients, negating one. We get the constant straightforwardly from the point we're going through:
4x + 5y = 4(-1)+5(3) = 11
Those lines meet at the foot of the perpendicular, which is what we're after.
4x + 5y = 11
5 x - 4y = 10
We eliminate y by multiplying the first by four, the second by five and adding.
16x + 20y = 44
25x - 20y = 50
41x = 94
x = 94/41
y = (11 - 4x)/5 = 15/41
We want the distance from (-1,3) to (94/41,15/41)
Answer: Our required probability is 0.175.
Step-by-step explanation:
Since we have given that
Average of 5 e-mails messages per day.
so,
We need to find the probability that on a randomly selected day your professor will have 5 messages.
Let X be the number of messages in poisson distribution.
So, P(X=5) is given by
Hence, our required probability is 0.175.